When I was younger I read this fantasy series involving two siblings who find out they are wizards. Their parents are involved to some extent but I think they are mostly learning from their uncle (maybe? a slightly older gentleman at least).

There are some things that I remember specifically including: that there is one scene in which the mother tells one of the children that they should always treat homeless people with kindness and give them any money they could. This is because sometimes homeless people were Angels who would watch over you after showing selflessness; in one of the books there is a detailed description of the hanging gardens of Babylon in which they are residing at the time. Another thing I remember is that wizards were capable of drawing perfect circles and lines because of their use in many spells.

I am pretty sure that it was a trilogy, or maybe when I read it there were only three books written, I think I read them sometime between 2006-2010.

1 Answer
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This immediately reminded me of when I read the first volume of the "Children of the Lamp" series by P. B. Kerr. I did a little Googling just now to confirm my very vague recollections. (If you click on the series title, the link will take you to Wikipedia's detailed entry on the entire series.)

Here are some points of correspondence between your description and what I can confirm from other sources:

When I was younger I read this fantasy series involving two siblings who find out they are wizards.

The co-stars of the series are John and Philippa Gaunt, twins who are 12 years old as the series starts.

Their parents are involved to some extent but I think they are mostly learning from their uncle (maybe? a slightly older gentleman at
least).

The Wikipedia entry for the series says:

During an operation to get the wisdom teeth removed, they both have
the same dream in which their uncle, Nimrod, asks that they come to
London. He tells them that they are djinn (genies).

The Wikipedia entry also confirms (as I thought I remembered) that the twins' mother tried her best to live as a normal person (i.e. zero use of magic powers) after she married her non-magical husband and settled down to raise children with him. Which explains why her brother Nimrod is the one who takes the lead in teaching the kids about magic when they're old enough to benefit from the instruction.

There are some things that I remember specifically including: that there is one scene in which the mother tells one of the children that
they should always treat homeless people with kindness and give them
any money they could because sometimes homeless people were Angels who
would watch over you after showing selflessness;

I can't swear that I remember that bit of advice from their mother (although you may well be right), but a little Googling found this in a character entry on the Wiki dedicated to the series:

Afriel was an angel, disguised as a homeless person, who met John and
Philippa in the third book.

Also:

in one of the books there is a detailed description of the hanging gardens of Babylon in which they are residing at the time.

I cannot swear to the "detailed description" part, but Book 2 is titled The Blue Djinn of Babylon and some Googling tells me that it does, in fact, involve a visit to the famous Hanging Gardens.

I am pretty sure that it was a trilogy, or maybe when I read it there were only three books written, I think I read them sometime
between 2006-2010.

Wikipedia says Book 1 came out in 2004, and Books 2 and 3 came out in 2006. So if you first noticed the series around late 2006, there would have been just three volumes available in bookstores and libraries at that time. (But the full series only ended when Book 7 was released in 2011.)

I was also reminded of the Children of the Lamp. There are many similarities. The two big sticking points are that A) John and Philippa are Djinn, not wizards, and B) from what I can recall they never used diagrams for casting magic - magic was mostly done using "magic words" (like Abracadabra)
– Arcanist LupusJan 17 '18 at 4:00

@ArcanistLupus - No, that plot point is there too. Djinn in the series can draw straight lines, circles, etc. better than humans.
– AdamantJan 17 '18 at 4:30

@Arcanist Lupus -- You may call A) a "big sticking point," but I saw it as "a trivial discrepancy." In other words, I never got the impression that Goose11999 was swearing that the exact word "Wizard" was used repeatedly in the text of the books. Only that the two kids learned they had inherent magical ability, and Goose11999 simply used the word "wizard" to describe the general impression left in his (or her?) memory after a decade or so. The actual text easily could have called the kids "mages" or "sorcerers" or "Deryni" or "Comyn" or "channelers" or "djinn" or something else entirely.
– LorendiacJan 18 '18 at 0:29

@Lorendiac - My wording was imprecise. Those two points are the details at which the descriptions varied the most - I didn't mean to imply that I thought that they invalidated the answer. That said, I saw A) as being more significant because the fact that John and Philippa are Djinn is the primary premise of the series (hence the series title "Children of the Lamp"), so it seems like an significant detail to be misremembered.
– Arcanist LupusJan 18 '18 at 2:21

@Arcanist Lupus -- you want the truth? The only reason I remembered that "djinni" or "genies" had anything to do with the plot was the fact that I distinctly remembered the series title was "Children of the Lamp" -- evocative of Aladdin's Lamp from the Arabian Nights. If not for that, I might just have thought, "Didn't those twins discover that there was some sort of magical heritage on one side of their family tree?" On this site, I've learned to never underestimate just how much colorful detail the human memory is capable of forgetting about a story that was read 10 or 20 years ago.
– LorendiacJan 19 '18 at 3:03